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zlantp.f
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1 *> \brief \b ZLANTP
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZLANTP + dependencies
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11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlantp.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlantp.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIAG, NORM, UPLO
25 * INTEGER N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION WORK( * )
29 * COMPLEX*16 AP( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZLANTP returns the value of the one norm, or the Frobenius norm, or
39 *> the infinity norm, or the element of largest absolute value of a
40 *> triangular matrix A, supplied in packed form.
41 *> \endverbatim
42 *>
43 *> \return ZLANTP
44 *> \verbatim
45 *>
46 *> ZLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47 *> (
48 *> ( norm1(A), NORM = '1', 'O' or 'o'
49 *> (
50 *> ( normI(A), NORM = 'I' or 'i'
51 *> (
52 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53 *>
54 *> where norm1 denotes the one norm of a matrix (maximum column sum),
55 *> normI denotes the infinity norm of a matrix (maximum row sum) and
56 *> normF denotes the Frobenius norm of a matrix (square root of sum of
57 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58 *> \endverbatim
59 *
60 * Arguments:
61 * ==========
62 *
63 *> \param[in] NORM
64 *> \verbatim
65 *> NORM is CHARACTER*1
66 *> Specifies the value to be returned in ZLANTP as described
67 *> above.
68 *> \endverbatim
69 *>
70 *> \param[in] UPLO
71 *> \verbatim
72 *> UPLO is CHARACTER*1
73 *> Specifies whether the matrix A is upper or lower triangular.
74 *> = 'U': Upper triangular
75 *> = 'L': Lower triangular
76 *> \endverbatim
77 *>
78 *> \param[in] DIAG
79 *> \verbatim
80 *> DIAG is CHARACTER*1
81 *> Specifies whether or not the matrix A is unit triangular.
82 *> = 'N': Non-unit triangular
83 *> = 'U': Unit triangular
84 *> \endverbatim
85 *>
86 *> \param[in] N
87 *> \verbatim
88 *> N is INTEGER
89 *> The order of the matrix A. N >= 0. When N = 0, ZLANTP is
90 *> set to zero.
91 *> \endverbatim
92 *>
93 *> \param[in] AP
94 *> \verbatim
95 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
96 *> The upper or lower triangular matrix A, packed columnwise in
97 *> a linear array. The j-th column of A is stored in the array
98 *> AP as follows:
99 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
100 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
101 *> Note that when DIAG = 'U', the elements of the array AP
102 *> corresponding to the diagonal elements of the matrix A are
103 *> not referenced, but are assumed to be one.
104 *> \endverbatim
105 *>
106 *> \param[out] WORK
107 *> \verbatim
108 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
109 *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
110 *> referenced.
111 *> \endverbatim
112 *
113 * Authors:
114 * ========
115 *
116 *> \author Univ. of Tennessee
117 *> \author Univ. of California Berkeley
118 *> \author Univ. of Colorado Denver
119 *> \author NAG Ltd.
120 *
121 *> \date November 2011
122 *
123 *> \ingroup complex16OTHERauxiliary
124 *
125 * =====================================================================
126  DOUBLE PRECISION FUNCTION zlantp( NORM, UPLO, DIAG, N, AP, WORK )
127 *
128 * -- LAPACK auxiliary routine (version 3.4.0) --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * November 2011
132 *
133 * .. Scalar Arguments ..
134  CHARACTER diag, norm, uplo
135  INTEGER n
136 * ..
137 * .. Array Arguments ..
138  DOUBLE PRECISION work( * )
139  COMPLEX*16 ap( * )
140 * ..
141 *
142 * =====================================================================
143 *
144 * .. Parameters ..
145  DOUBLE PRECISION one, zero
146  parameter( one = 1.0d+0, zero = 0.0d+0 )
147 * ..
148 * .. Local Scalars ..
149  LOGICAL udiag
150  INTEGER i, j, k
151  DOUBLE PRECISION scale, sum, value
152 * ..
153 * .. External Functions ..
154  LOGICAL lsame
155  EXTERNAL lsame
156 * ..
157 * .. External Subroutines ..
158  EXTERNAL zlassq
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC abs, max, sqrt
162 * ..
163 * .. Executable Statements ..
164 *
165  IF( n.EQ.0 ) THEN
166  value = zero
167  ELSE IF( lsame( norm, 'M' ) ) THEN
168 *
169 * Find max(abs(A(i,j))).
170 *
171  k = 1
172  IF( lsame( diag, 'U' ) ) THEN
173  value = one
174  IF( lsame( uplo, 'U' ) ) THEN
175  DO 20 j = 1, n
176  DO 10 i = k, k + j - 2
177  value = max( value, abs( ap( i ) ) )
178  10 CONTINUE
179  k = k + j
180  20 CONTINUE
181  ELSE
182  DO 40 j = 1, n
183  DO 30 i = k + 1, k + n - j
184  value = max( value, abs( ap( i ) ) )
185  30 CONTINUE
186  k = k + n - j + 1
187  40 CONTINUE
188  END IF
189  ELSE
190  value = zero
191  IF( lsame( uplo, 'U' ) ) THEN
192  DO 60 j = 1, n
193  DO 50 i = k, k + j - 1
194  value = max( value, abs( ap( i ) ) )
195  50 CONTINUE
196  k = k + j
197  60 CONTINUE
198  ELSE
199  DO 80 j = 1, n
200  DO 70 i = k, k + n - j
201  value = max( value, abs( ap( i ) ) )
202  70 CONTINUE
203  k = k + n - j + 1
204  80 CONTINUE
205  END IF
206  END IF
207  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
208 *
209 * Find norm1(A).
210 *
211  value = zero
212  k = 1
213  udiag = lsame( diag, 'U' )
214  IF( lsame( uplo, 'U' ) ) THEN
215  DO 110 j = 1, n
216  IF( udiag ) THEN
217  sum = one
218  DO 90 i = k, k + j - 2
219  sum = sum + abs( ap( i ) )
220  90 CONTINUE
221  ELSE
222  sum = zero
223  DO 100 i = k, k + j - 1
224  sum = sum + abs( ap( i ) )
225  100 CONTINUE
226  END IF
227  k = k + j
228  value = max( value, sum )
229  110 CONTINUE
230  ELSE
231  DO 140 j = 1, n
232  IF( udiag ) THEN
233  sum = one
234  DO 120 i = k + 1, k + n - j
235  sum = sum + abs( ap( i ) )
236  120 CONTINUE
237  ELSE
238  sum = zero
239  DO 130 i = k, k + n - j
240  sum = sum + abs( ap( i ) )
241  130 CONTINUE
242  END IF
243  k = k + n - j + 1
244  value = max( value, sum )
245  140 CONTINUE
246  END IF
247  ELSE IF( lsame( norm, 'I' ) ) THEN
248 *
249 * Find normI(A).
250 *
251  k = 1
252  IF( lsame( uplo, 'U' ) ) THEN
253  IF( lsame( diag, 'U' ) ) THEN
254  DO 150 i = 1, n
255  work( i ) = one
256  150 CONTINUE
257  DO 170 j = 1, n
258  DO 160 i = 1, j - 1
259  work( i ) = work( i ) + abs( ap( k ) )
260  k = k + 1
261  160 CONTINUE
262  k = k + 1
263  170 CONTINUE
264  ELSE
265  DO 180 i = 1, n
266  work( i ) = zero
267  180 CONTINUE
268  DO 200 j = 1, n
269  DO 190 i = 1, j
270  work( i ) = work( i ) + abs( ap( k ) )
271  k = k + 1
272  190 CONTINUE
273  200 CONTINUE
274  END IF
275  ELSE
276  IF( lsame( diag, 'U' ) ) THEN
277  DO 210 i = 1, n
278  work( i ) = one
279  210 CONTINUE
280  DO 230 j = 1, n
281  k = k + 1
282  DO 220 i = j + 1, n
283  work( i ) = work( i ) + abs( ap( k ) )
284  k = k + 1
285  220 CONTINUE
286  230 CONTINUE
287  ELSE
288  DO 240 i = 1, n
289  work( i ) = zero
290  240 CONTINUE
291  DO 260 j = 1, n
292  DO 250 i = j, n
293  work( i ) = work( i ) + abs( ap( k ) )
294  k = k + 1
295  250 CONTINUE
296  260 CONTINUE
297  END IF
298  END IF
299  value = zero
300  DO 270 i = 1, n
301  value = max( value, work( i ) )
302  270 CONTINUE
303  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
304 *
305 * Find normF(A).
306 *
307  IF( lsame( uplo, 'U' ) ) THEN
308  IF( lsame( diag, 'U' ) ) THEN
309  scale = one
310  sum = n
311  k = 2
312  DO 280 j = 2, n
313  CALL zlassq( j-1, ap( k ), 1, scale, sum )
314  k = k + j
315  280 CONTINUE
316  ELSE
317  scale = zero
318  sum = one
319  k = 1
320  DO 290 j = 1, n
321  CALL zlassq( j, ap( k ), 1, scale, sum )
322  k = k + j
323  290 CONTINUE
324  END IF
325  ELSE
326  IF( lsame( diag, 'U' ) ) THEN
327  scale = one
328  sum = n
329  k = 2
330  DO 300 j = 1, n - 1
331  CALL zlassq( n-j, ap( k ), 1, scale, sum )
332  k = k + n - j + 1
333  300 CONTINUE
334  ELSE
335  scale = zero
336  sum = one
337  k = 1
338  DO 310 j = 1, n
339  CALL zlassq( n-j+1, ap( k ), 1, scale, sum )
340  k = k + n - j + 1
341  310 CONTINUE
342  END IF
343  END IF
344  value = scale*sqrt( sum )
345  END IF
346 *
347  zlantp = value
348  RETURN
349 *
350 * End of ZLANTP
351 *
352  END